y^{''}-y^'+2y=2e^{2t}+5t-1

Lösung

y^{^{''}} - y^{^{'}} + 2 y = 2 e^{2 t} + 5 t - 1

y = e^{\frac{t}{2}} (c_{1} cos (\frac{7 t}{2}) + c_{2} sin (\frac{7 t}{2})) + \frac{3}{4} + \frac{e ^{2 t} + 5 t}{2}

Schritte zur Lösung

y^{''} (t) - y^{'} (t) + 2 y = 2 e^{2 t} + 5 t - 1

Solve linear ODE:

y = e^{\frac{t}{2}} (c_{1} cos (\frac{7 t}{2}) + c_{2} sin (\frac{7 t}{2})) + \frac{3}{4} + \frac{e ^{2 t} + 5 t}{2}

y = e^{\frac{t}{2}} (c_{1} cos (\frac{7 t}{2}) + c_{2} sin (\frac{7 t}{2})) + \frac{3}{4} + \frac{e ^{2 t} + 5 t}{2}

y^{^{''}} + y^{^{'}} + y = k

4 y^{^{''}} - y = e^{\frac{1}{2} x} + 7

y^{^{''}} - y^{^{'}} + y = 2

y^{^{''}} + 49 y = - 5 cos (7 t + π^{3}), y (0) = 0, y^{^{'}} (0) = 0

y^{^{''}} - 8 y^{^{'}} + 16 y = e^{4 x} \cdot ln (9 + x^{2})